1. Until recently, senescence was assumed to be a universal phenomenon. Evolutionary theories of senescence predict that no organism may escape the physiological decline that results in an increase in mortality risk and/or decline in fertility with age. However, evidence both in animals and plants has emerged in the last decade defying such predictions. Researchers are currently seeking mechanistic explanations for the observed variation in ageing trajectories. 2. We argue that the historical view on the inevitability of senescence is due, in part, to the development of its classical theories, which targeted primarily unitary organisms. In unitary species, the integration of resources and functions is high, and adult size is determined. In contrast, the architecture of modular organisms is indeterminate and built upon repeated modules. The isolation of mortality risk in species like hydra (Hydra spp.) or creosote brush Larrea tridentata may explain their null or even negative senescence. 3. Caleb Finch hypothesized three decades ago that species with the ability to compartmentalize risk may escape senescence. Here, we first review the evidence on organisms that slow down or even avoid senescence in the context of their architecture, along a continuum of unitarity-modularity. Then, we use openaccess databases to comparatively analyse various moments of senescence and link longevity to the degree of anatomical modularity. Our analysis compares the pace of senescence across 138 plants and 151 animals, and the shape of senescence across a subset of these. Our comparative analysis reveals that plant species that are more modular do indeed tend to escape from senescence more often than those that are unitary. The role of modularity in animal senescence is less clear. 4. In light of novel support for Finch's hypothesis across a large diversity of plant species, and with less conclusive findings in animals, we identify new research directions. We highlight the opportunities related to age-dependent mortality factors. Other areas for further research include the role of modularity in relation to endocrine actions, and the costs of modular anatomies.